| Taylor-Couette flow refers to the flow between two concentric rotating cylinders. The transition of laminar flow to turbulence and the related properties of flow field are an important research subject of Taylor-Couette flow. The flow between two rotating coaxial frustums has been investigated by many researchers using experimental observation and numerical simulation. However, most studies were based on the case of parallel gap. In fact, the case of non-parallel gap has not received deserved attention.The case of non-parallel gap is considered in this paper. The governing equations and the corresponding boundary conditions are given under the cylindrical coordinate system. The angle between the side of the inner frustum and the bottom plane is called the internal inclination angle, while the angle between the outer frustum and bottom plan is viewed as the external inclination angle, and their difference leads to the case of non-parallel gap. The numerical simulation has been carried out for different external inclination angles using the Fluent software. The calculation results are compared with the case of parallel gap in order to study the impact of the boundaries on the flow field.Next, a comparison between parallel and non-parallel case is made. The critical Reynolds number for the occurrence of the first Taylor vortex and the first pair of Taylor vortices, as well as for the fullness of Taylor vortices in the gap is obtained. The results show that the flow in the gap becomes more likely unstable and the occurrence of Taylor vortex is getting easier with the increase of the top gap size.Finally, the impact of the boundary on the flow in the case of non-parallel gap is studied. By defining different Reynolds number, the estimate of the critical Reynolds number for the occurrence of the first Taylor vortex and the fullness of Taylor vortices in the case of non-parallel gap are carried out. Based on the results for the case of parallel gap, the obtained estimate confirms the simulation results. |
